Electrocomponent Science and Technology
1974, Vol. 1, pp. 43-49
(C)
Gordon and Breach Science Publishers Ltd.
Printed in Great Britain
FREQUENCY SPECTRUM GENERATED BY
THYRISTOR CONTROL
J. K. HALL and N. C. JONES
Loughborough University of Technology, Loughborough, Leics. U.K.
(Received October 30, 1973; in final form December 19, 1973)
This paper describes the measured harmonics in the load currents of thyristor circuits and shows that with firing
angle control the harmonic amplitudes decrease sharply with increasing harmonic frequency, but that they extend
to very high harmonic orders of around 6000. The amplitudes of the harmonics are a maximum for a firing delay
angle of around 90
Integral cycle control produces only low order harmonics and sub-harmonics.
It is also shown that with firing angle control apparently random inter-harmonic noise is present and that the
harmonics fall below this noise level at frequencies of approximately 250 KHz for a switched 50 Hz waveform and
for the resistive load used. The noise amplitude decreases with increasing frequency and is a maximum with 90
firing delay.
inductance. 6,7 Literature on the subject tends to
assume that noise is due to the high frequency
harmonics generated by thyristor switch-on and the
design of suppression components is based on this.
This investigation has been performed in order to
establish the validity of this assumption, since it is
believed that there may be a number of perhaps
separate sources of noise in thyristor circuits. Four
well-known circuits have been examined, both
experimentally using a spectrum analyser and by a
theoretical analysis of the waveforms to define the
harmonic spectrum expected. The presence of
random noise, in addition to the expected harmonics,
INTRODUCTION
Thyristors are now widely used for control of power
in both d.c. and a.c. circuits. The advantages of
relatively small size, low losses and fast switching
speeds have contributed to the vast growth in
application since their introduction, when they were
basically a solid-state replacement for mercury-arc
rectifier devices. As a result, attention has been
focussed on the inherent problems produced by
thyristor control, some of which are a perpetuation
of those with mercury-arc rectifiers. These are now
giving cause for greater concern owing to the scale of
usage. The majority of applications utilise a.c. line
commutation and only these are considered here.
The switching action of the thyristors (or triac)
results in non-sinusoidal currents being drawn from
the a.c. supply system. Harmonics and noise are
thereby injected into the power supply and give rise,
to conducted interference with other electronic and
communications equipment. 2-4 Unless the apparatus
is screened, radiated interference also occurs. The
effects of interference are varied, from malfunctioning
of low-level micrologic circuits and triggering of other
separately-controlled thyristors to disturbance of
radio and T.V. reception, s The elimination of these
effects is an important objective. Ways of suppressing
the harmonics and noise have been devised using, on
the one hand, greatly improved discrete components
and on the other, composite devices containing
within one component resistance, capacitance and
is demonstrated.
2
EXPERIMENTAL DETAILS
The four single-phase circuits investigated were a
single-thyristor half-wave rectifier, a triac a.c. controller with firing angle control, a thyristor full-wave
rectifier bridge, and a triac a.c. controller with
integral cycle control. The triac functions as two
thyristors in anti-parallel, but has a single gate
electrode. The load current waveforms were examined and these have the form shown in Figure 1.
From the conducted interference viewpoint, the
supply current is of interest. The supply current is the
same as the load current in all circuits except the
rectifier bridge, in which case it has the same form as
that of the triac with firing angle control.
43
J.K. HALL
44
tesistive
load
Lc
Thyristor
Mains
circuit
Sampling resitor
No
counter
i o
__r-t,,
ooor
o00
Frequency
analy=er
FIGURE 2
Basic measuring circuit.
(d)
((1} Single thyristor, hall-wave rectifier.
b) Variable a.c. by trioc with firing angle control.
(c) Thyristor bridge, full-wove rectifier.
(d) Variable a.c. by triac with integral cycle control.
FIGURE
Output waveforms for the circuits
examined.
The basic measuring circuit is shown in Figure 2.
This consists of a resistive load of low inductance
supplied from single-phase a.c. mains through the
thyristor controller. In series with the load is a
sampling resistor of very low inductance, across
which a voltage proportional to load current is taken.
This is fed to a Hewlett-Packard spectrum analyser 8
and an oscilloscope. This arrangement is more suitable for study of the low frequency harmonics, since
combined symmetrical and asymmetrical radiofrequency components are indicated. For detailed
study of the radio-frequency voltages, the techniques
of BS 8009 are more appropriate. The complete test
circuit is installed in a screened room in order to
reduce external interference.
The principle of the spectrum analyser is that the
waveform under examination is swept by a narrowband filter (10 Hz minimum bandwidth) controlled
by a variable frequency oscillator. The output is
displayed on a storage tube whose vertical axis
represents amplitude, and horizontal axis frequency.
A typical trace is shown in Figure 3, where the
individual harmonics at 50 Hz intervals can easily be
seen. Controls on the analyser enable the bandwidth
of the filter, the swept frequency limits and sweep
time to be controlled. A variable attenuator adjusts the
input signal appropriately. The frequency counter
(Figure 2) gives a direct indication of the frequency
band being swept, thus enabling the specific harmonic
frequencies displayed to be interpreted. It should be
noted that the spectrum analyser indicates the
magnitudes of the harmonics present in the waveform, but not their phase in relation to the
fundamental.
Zdro
frequency,
FIGURE 3
Harmonic
frequency .(’500 HZ/C rn,)
Harmonic spectrum trace from the
spectrum analyser.
45
THYRISTOR FREQUENCY SPECTRUM
THEORETICAL CONSIDERATIONS
3
B1
The current waveforms of Figure can be resolved
into the harmonic components present by use of the
general Fourier Series:n--c
E
Ao + n:l
fit)
C n sin(not. + n)
rr--&+
2
2n
where a is the firing delay angle,
and ] is the peak value of the sinusoidal current.
b) Triac with firing delay:
nth harmonic of the supply frequency (n
where f(t) is the waveform function under consideration,
n is the harmonic order- 1,2,3
Ao is the direct component
Cn is the amplitude of the nth harmonic
is the phase of the nth harmonic.
n
An
][cos(n+l)t
cos(n-1)a
2
n-1
n2-1
n+l
7r
Cn (An 2 + Bn
where
]
l[sin(n+ sin(n-1)o]
1)o
n+l
n-1
n
Even harmonics are absent, since An
n 2,4,6,... during the derivation.
The expansion is calculated from:
3,5,7,...):
Bn
0 th
d.c. component:
Ao
fit) cos n cot d(cot)
0
fundament:
and
]
[cos2-l]
[ 2a]
2
fit) sin n cot d(ot)
sin
n
B1
An
Bn
tan -1
2
c) Full-wave rectifier:
nth harmonic of the supply frequency (n
The mean or d.c. level is given by:
2r
Ao
2n
The constants An,
as follows:
o
Bn
An
fit) dt
|
and
Ao
a) Half-wave rectifier:
An
1" [cos(1 + n)ot cos(1
27r
[
]
+n
+ n)a
Bn=- [sin(-+n
d.c. component:
Ao
2r
(cos ot + 1)
fundamental:
A
2r
[cos
+
2,3,4,...):
n)ot 2(-1) n]
+
n
sin(1
n)a]
-n
cos(1-2n)a
+
1-2n
l+2n
+ 2n)a
[sin(1
n k i +2n
for each waveform are
nth harmonic of the supply frequency (n
rr
[cos(l+2n)a
2,4,6,...):
sin(1
2
+z
1-4n
]
2n)a]
1-
Odd harmonics are absent, since An
during the derivation.
3,5,7,
Bn
0 with
n
d.c. conponent:
n]
[1 + cos a]
Ao
fundamental:
A1 =B1 =0
d) Triac with &tegral-cycle control:
nth harmonic of the output waveform (n
T, 3T, 5T,...):
An
iT
rr(n
2
T
2) [
cos
(2nrrN)
T
]
1,2,3,...
J.K. HALL
46
TABLE
Measured harmonic amplitudes (as a % of mains) with varying firing angle for the
half-wave rectifier circuit.
Amplitude at the stated harmonic frequency (Hz)
Firing angle a
50
Bn
(Degrees)
(fundamental)
18
54
90
126
162
50.0
43.0
28.0
11.0
1.3
iT
rr(n
2
T 2)
sin
100
(2nd)
150
(3rd)
22.0
27.0
23.0
10.0
1.5
1.4
10.0
15.0
9.0
1.8
(2nrN)
a)
T
Putting n
gives the coefficients for the fundamental frequency at the load; that is, the lowest
subharmonic of the supply frequency (= 1/T x supply
frequency). Other coefficients are given for frequencies up to that of the supply voltage. The coefficients for the supply frequency harmonic of the
load current (n T):
AT =0
^N
BT I-T
For higher frequencies:
An B n =0
for harmonics which are even multiples of the supply
frequency (n 2T, 4T, 6T,...).
d.c. component:
Ao
0
where T is the number of supply cycles in a period of
integral-cycle control, and N is the number of ’ON’
cycles in a period of integral-cycle control. The
individual harmonic amplitudes Cn and phases,
(when required) were calculated with the aid of a
computer for assumed values of n and firing delay a
or on/off cycle ratio, as appropriate.
n
4
RESULTS AND DISCUSSION
It is appropriate to consider the low frequency and
high frequency harmonic components of the current
waveforms separately. The individual thyristor circuits
are taken in order.
500
(10th)
1.0
2.4
3.0
2.5
1.0
1000
(20th)
2000
(40th)
0.4
1.0
1.2
1.0
0.4
0.20
0.45
0.60
0.45
0.20
Thyristor Half-Wave Rectifier
The results of measurements of specific low
frequency harmonics generated with the single
thyristor control are given in Table I. They are shown
as a function of firing angle and it is apparent that the
harmonics are a maximum with a firing delay of 90
A detailed representation of the harmonics present up
to 1900 Hz with a firing delay of 90 is shown in
Figure 4. Both measured and computed values are
given; it can be seen that these agree very well.
Measurements of the high frequency components
up to 300 kHz were made. the spectrum analyser
indicated the presence of random noise between the
predicted lines of the harmonic spectrum. Table II
summarises the measured amplitudes of the harmonics at 50 kHz and 100 kHz, together with the
interharmonic noise level near these frequencies, both
as a function of firing angle. As is to be expected
from the low frequency harmonic results, the high
frequency harmonics have a maximum amplitude
with the firing angle set at 90 However, the same is
true of the noise, within experimental error, though
the effect is not so pronounced. Table III shows
measurements of harmonics and noise up to the
TABLE II
Dependence of high frequency harmonics and noise on firing
angle for the half-wave rectifier circuit.
(Values in uV across a ohm sampling resistor; 0.7 V obtained
with full mains applied)
At frequency 50 kHz
At frequency 100 kHz
Firing angle
(Degrees)
Harmonics
Noise
Harmonics
Noise
18
54
90
126
162
20
60
80
70
35
8
15
15
15
8
2
20
30
25
12
2
8
8
10
5
47
THYRISTOR FREQUENCY SPECTRUM
I00
80-
60-
40-
o
s6o
200
,ooo
,.bo
doo
Amplitude values x I0
xl
Harmonic frequency (Hz
Measured on the Spectrum Analyser
Computed values using Fourier Analysis
FIGURE 4
Low-frequency harmonics from the half-waverectifier ckcuit (90 firing delay).
TABLE III
Measured high frequency harmonic amplitudes and noise for
the half-wave rectifier circuit with 90 firing delay.
(Amplitudes in uV across a 5 ohm sampling resistor:
3.7V obtained with full mains applied).
Frequency
(kHz)
order
10
30
60
100
130
160
200
230
260
300
200
600
1200
2000
2600
3200
4000
4600
5200
6000
Harmonic
Harmonic
amplitude
Noise
amplitude
4000
1000
300
150
110
70
50
40
0
100
30
25
20
20
20
15
15
10
10
highest frequencies considered. Both harmonics and
noise decrease with increasing harmonic order,
though the noise decreases at a much lesser rate. At
about 300 kHz the harmonic amplitudes are such that
they cannot be distinguished from the noise.
b) Triac with Firing Delay
Measurements similar to those made with the single
thyristor were repeated for the triac a.c. controller
and the results are shown in Tables IV and V. Table
IV demonstrates again that the harmonic amplitudes
are a maximum with 90 firing delay. As predicted by
the Fourier Analysis, only odd harmonics are present
owing to the symmetry of positive and negative
half-cycles (Figure b). Table V again illustrates the
decreasing harmonic and noise amplitudes with increasing harmonic frequency and the merging of the
harmonics into the noise around 300 kHz.
TABLE IV
Measured harmonic amplitudes (as a % of mains) with varying firing angle for the
triac circuit.
Amplitude at the stated harmonic frequency <Hz)
Firing angle
(Degrees)
18
54
90
126
162
50
(fundamental)
150
(3rd)
250
(5th)
550
(1 lth)
98
90
58
48
2
4
18
30
18
2
3.0
10.0
10.0
10.0
2.5
2.0
3.5
9.0
4.5
1.9
1050
(21st)
1.0
1.8
3.5
1.5
0.5
2050
(4 lst)
0.4
1.0
1.2
1.0
0.4
J.K. HALL
48
TABLE V
Measured high frequency harmonic amplitudes and noise
for the triac circuit with 90 firing delay. (Amplitudes in
tV across a 5 ohm sampling resistor; 3.7 V obtained with
full mains applied).
Frequency
(kHz)
order
Approx. harmonic Harmonic
amplitude
10
30
60
100
130
160
200
230
260
200
600
1200
2000
2600
3200
4000
4600
5200
3500
800
250
140
80
80
50
30
Noise
amplitude
100
50
40
40
40
30
25
25
20
Thyristor Full-Wave Rectifier
The low-order harmonics measured in the d.c. load
current waveforms (Figure c) are shown in Table V1
as a function of firing angle. Only even harmonics of
the supply frequency are present, 100 Hz being the
fundamental ripple frequency. The harmonics of this
ripple frequency exhibit their maxima at 90 firing
delay. As mentioned earlier, the a.c. line current
drawn has the same waveform as is produced by triac
control (Figure lb), so that Tables IV and V provide
the relevant information for the rectifier supply
current.
d) Triac with Integral-Cycle Control.
The zero-voltage switching of integral-cycle control
results in the absence of high frequency harmonics,
and herein lies the advantage of the method. This is
illustrated in Figure 5 which shows results obtained
with equal on and off periods. Change in the ratio
on/off cycles will produce a variation in harmonic
amplitudes, but the general pattern of a predominance of low order harmonics and subharmonics of the
supply frequency is well demonstrated. The presence
c)
ofsubharmonics is disadvantageous with loads of a low
thermal time constant, for which this method of
control may be inappropriate. No measurements have
been taken at the high frequency end of the spectrum.
Only measured results have been quoted in most
cases since Figure 4 shows that these agree fairly
closely with those computed from the Fourier
Analysis. An infinite rate of current rise at thyristor
turn-on with firing angle control has been assumed
for the analysis though this is not attained in practice.
For this reason the correlation is less good at the
higher frequencies. The presence of the interharmonic
noise with firing angle control is the most outstanding
feature observed. The fact that this exceeds the
harmonics at frequencies above about 260 kHz is very
significant. Tests with the single thyristor in circuit,
with the triggering signal removed, and carrying d.c.
revealed only minimal noise, showing that most of
the noise is generated by the thyristor control and
not the sampling resistor or other peripheral equipment.
5
CONCLUSIONS
The measurements have confirmed the presence of
harmonics in the load currents of the thyristor
circuits examined and have defined their pattern. With
firing angle control the harmonic amplitudes decrease
sharply with increasing harmonic frequency but they
extend to very high harmonic orders or around 6000.
The amplitudes of the harmonics measured are a
maximum for a firing delay angle of around 90
though this does not necessarily apply to all
the harmonics present. 1 Integral cycle control
produces only low-order harmonics and subharmonics. Computed results have not been given in
every case as correlation with measurements is good,
though this is less so at the highest frequencies. With
firing angle control, apparently random, inter-
,
TABLE VI
Measured harmonic amplitudes (as a % of mains) with varying firing angle
for the full-wave bridge circuit.
Firing angle a
(Degrees)
18
54
90
126
162
Amplitude at the stated harmonic frequency (Hz)
100
(2nd)
200
(4th)
300
(6th)
500
(10th)
1000
(20th)
2000
(40th)
50.0
60.0
45.0
18.0
2.5
12.0
12.0
20.0
15.0
2.5
6.0
11.0
12.0
11.0
2.5
2.0
5.5
7.0
4.0
2.0
1.5
3.5
4.0
2.5
1.2
0.6
1.4
1.5
1.5
0.5
49
THYRISTOR FREQUENCY SPECTRUM
I00
Illlllllllll[lllllil
20
40
60
Harmonic frequency.
FIGURE 5
2ha
;20
(Hz)
Harmonics from the integral-cycle a.c. control circuit (25:25 cycles on/off ratio).
harmonic noise is present, the harmonics falling
below this noise level at frequencies of approximately
250 kHz-300 kHz, for the resistive load used. The
noise amplitude decreases with increasing frequency
and is a maximum with 90 firing delay. Investigation
into the causes of noise generated by thyristor
control is continuing.
REFERENCES
2
3
4
5
F.E. Gentry et al., Semiconductor Controlled Rectifiers,
(Prentice-Hall 1964).
J.R. Taylor et al., Electronic Engineering, 43, 37-41
(August, 1971).
D.W. Matthias, IEEE Electromagnetic Compatibility
Symposium Record, 29-34 (June, 1969).
A. A. Collie, lEE Electronics and Power, 18, 19-22
(January, 1972).
SCR Manual (5th Edition) General Electric Co. Chap.
17.
P.J. Harrop, Electron, No. 19, 13-14 (11 January,
1973).
7 H.P. Kaiserworth, Siemens Electronics Component
Bulletin, VII, 49-52 (1972).
8 R. C. Keiter, Hewlett--Packard Journal 23, (1), 4-9
6
ACKNOWLEDGEMENT
Acknowledgement is made of the experimental facilities
provided by the Department of Electronic and Electrical
Engineering, Loughborough University of Technology. The
advice and encouragement of Professor D. S. Campbell is
greatly appreciated.
(September, 1971).
9 BS800, Parts and 3, 1972.
10 R. Smith, Electronic Engineering, 36, (442) 832-837
(1964).
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